Question 1138294
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<pre>
In this problem, concentrations are the ratios of the pure vinegar volume to the total volume.



Let x be the amount of the 9%  vinegar needed (in milliliters), and

let y be the amount of the 14%  vinegar needed.



The amount of the "pure" vinegar in the 9% mixture  is 0.09x mL.

The amount of the "pure" vinegar in the 14% mixture is 0.14y mL.

The resulting mixture contains  0.09x + 0.14y mL of the pure vinegar and has the volume of 310 mL.


Thus you have these two equations


    x + y = 310    milliliters           (1)    (the total volume)

    {{{(0.09x + 0.14y)/310}}} = 0.13.                 (2)    (the resulting mixture concentration)



From equation  (1), express  x = 310 - y.  Substitute it into equation (2) and multiply both sides of this equation by 310. 
You will get


    0.09*(310-y) + 0.14y = 0.13*310.


From the last equation express y and calculate


    y = {{{(0.13*310 - 0.09*310)/(0.14-0.09)}}} = 248 mL of the 14% vinegar are needed.


Then from equation (1),  x = 310 - 248 = 62 mL of the 9% vinegar are needed.


<U>Answer</U>. 248 mL of the 14% vinegar  and  62 mL of the 9% vinegar are  needed.


<U>Check</U>.  {{{(0.14*248 + 0.09*62)/310}}} = 0.13 = 13%.   ! Correct concentration !
</pre>

The problem is just solved.

I used 2-equation setup and the Substitution method.


There are other solution methods, too.


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There is entire bunch of introductory lessons covering various types of mixture problems

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Mixture-problems.lesson>Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/More-Mixture-problems.lesson>More Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Solving-typical-mixture-problems.lesson>Solving typical word problems on mixtures for solutions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-antifreeze-solutions.lesson>Word problems on mixtures for antifreeze solutions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-alloys.lesson>Word problems on mixtures for alloys</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Typical-word-problems-on-mixtures-from-the-archive.lesson>Typical word problems on mixtures from the archive</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Advanced-mixture-problems.lesson>Advanced mixture problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Advanced-mixture-problem-for-three-alloys.lesson>Advanced mixture problem for three alloys</A> 

in this site.


You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, &nbsp;from very detailed to very short.


Read them and become an expert in solution mixture word problems.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook in the section "<U>Word problems</U>" under the topic "<U>Mixture problems</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.